


CONCERNING THE PROCESS OF THRUST FAULTING 


TERENCE T. QUIRKE 
University of Illinois 


The following paper is offered as a contribution to the studies 
of low-angle faulting which have been led by the researches and 
teaching of Professor R. T. Chamberlin. 

A comparison of this paper with previous publications, espe- 
cially ““Low-Angle Faulting,” by R. T. Chamberlin and W. Z. 
Miller,’ will show that the writer has followed Chamberlin in large 
measure. Most of the material here presented has really been 
anticipated in the article referred to, but a different manner of 
approach on some phases of the study is attempted, and the 
possibility is suggested that there may be a closer relationship 
between low- and high-angle thrust faults than is commonly 
accepted. 

In 1910 Chamberlin? published his paper on the structure of 
. the Appalachian Mountains in which he showed reason to believe 
that the part of the crust affected by deformation is a shallow, 
wedge-shaped mass about thirty miles deep and about nine hundred 
miles long. Willis,’ upon independent but similar arguments, sug- 
gested that the depth of the mass deformed in the uplift of the 
Cascades lies between thirty-seven and one-half and fifteen hun- 
dred miles. 

So far as the writer knows, these conclusions have been accepted 
as sound, in spite of the fact that they appear to be fundamentally 
different from the prevalent notion that mountain folding is rela- 
tively shallow and that the deformable crust of the earth is of the 


1 Jour. Geol., XXVI (1918), 1-44. 


?R. T. Chamberlin, “Appalachian Folds of Central Pennsylvania,” Jour. Geol., 
XVIII (1910), 228-51. 


3 Bailey Willis, U.S, Geol. Surv., Prof. Paper No. 19 (1903),,p. 97. 
417 


418 TERENCE T. QUIRKE 


character of a thin layer or sheet. In a later paper Chamberlin’ 
concludes as the result of his work in the Rocky Mountains that 
the western mountain mass has this generic difference from the 
eastern range in that it is composed of broadly folded members 
of very great depth as contrasted with severely folded and faulted 
members of less depth. Thus following Chamberlin, it seems 
that there ate some cases of mountain folding in which the strains 
are relatively shallow as well as some cases in which deformation 
has been much deeper, which may support the theory that faulting 
and sharp folding may affect a shallow terrain at the same time that 
deeper parts of the crust are undergoing flow deformation. ‘The 
observation of Daly? that in south central British Columbia the 
overlying sediments are much more sharply folded than the under- 
lying pre-Cambrian rocks gives further support to this general 
notion. 

In attempting to analyze earth deformation it is natural, 
erroneously, to consider the deformed parts of the crust as com- 
prising the whole members subjected to stress; whereas such parts 
are merely those portions of the structural member which failed. 
In consequence of this, it follows that it is a matter of considerable 
doubt as to what the nature and dimensions of the structual mem- 
bers may have been. So it comes about that most discussions are 
based upon an attempted analysis of the strains involved rather 
than upon the basis of controlling forces. And this is logical 
enough, in that here and there the strains remain clearly recorded, 
whereas the stresses and the nature of the members involved can 
only be inferred. Presumably, if we follow the traditional teach- 
ings, the compressive forces are caused by a more rapid decrease 
in volume of the inner part of the earth than can be accompanied 
by the solid shell without buckling or breaking, and consequently 
the whole shell of the earth constitutes the members concerned. 
However, the earth’s crust is sharply divided into continental and 
oceanic members; whether these members are conceived to be 


™R. T. Chamberlin, ‘‘The Building of the Colorado Rockies,” Jour. Geol., XX VII 
(1919), 248. 

R.A. Daly, quoted by C. K. Leith, Structural Geology (1913), p. 127. 

3 Cf, Chamberlin and Miller, op. cit., p. 21. 


CONCERNING THE PROCESS OF THRUST FAULTING 419 


segments or sectors, according to the older and the newer theories 
respectively, they act as individual components of a single mem- 
ber and as such are subject to separate analyses. Curved, rigid, 
sheetlike members under lateral compression fail in the center. 
Apparently the earth members fail by rupture and buckling at 
the ends or edges,’ from which it follows, either that the conception 
of sheetlike members is erroneous, or that the members are not 
rigid bodies, or both. It is surely a fact that the earth members 
are not rigid under the conditions of mountain folding; the manner 
of their failure proves that beyond question. ‘There is still a pos- 
sibility that under some conditions the forces are transmitted 
through shell-like members, and that at other times the forces 
are distributed throughout deep earth sectors. It seems to be 
probable that both conditions have prevailed repeatedly at differ- 
ent times. Chamberlin’s conclusion that the mountain ranges 
are of two generic types, one with deep and the other with shallow 
roots, supports this idea. But, however deep the strains may be, 
it is possible that there is so distinct a zone of shearing between 
the frangible, nearly rigid crust and the interior which is deformed 
by flow that the crustal part in any case fairly may be considered 
an individual member. It is probable that deep-seated strains 
affect a discontinuous member, plastico-rigid at depth, but more 
frangible toward the surface,? wherefore the term “‘plastico- 
frangible,’ perhaps, might be used to denote the characteristic 
quality of the outer crust. Objections to these terms arise readily, 
especially by comparison with the terminology of other writers. 
T. C. Chamberlin prefers the term “‘elastico-rigid’’’ because that 
expression indicates rigidity associated with elasticity in distinc- 
tion from solidity due to high viscosity. The word ‘‘fluidable’’4 
has been used to denote the potential fluidity of the earth’s interior. 


1 Bailey Willis, ‘‘Mechanics of Appalachian Structure,” 13th Ann. Rept. U.S. 
Geol. Surv., Part II (1893), Be 247) 

2 Cf. Bailey Willis, U.S. Geol. Surv., Prof. Paper No. 19 (1903), p. 97, and Joseph 
Barrell, Jour. Geol., XXIII (1915), 438. 


3'T. C. Chamberlin, Jour. Geol., XXVI (1918), p. 194, and personal communi- 
cations. 


weit 


4J. W. Gregory, Geology of Today (London, 1915), p. 156. 


420 TERENCE T. QUIRKE 


But in this article there is no design either to emphasize the elas- 
ticity of the earth as a whole or the liquefaction of local parts, nor 
on the other hand is there any need to deny the reality of these 
characteristics. But inasmuch as no term has yet been devised 
which adequately describes the character of the earth’s interior, 
it is necessary to choose for different purposes different terms 
emphasizing different phases of the earth’s behavior, each admis- 
sible term being complementary and not contradictory to the 
others. 


TERRESTRIAL FORCES AND CRUSTAL MEMBERS 


The nature of earth stresses —The usual argument is that there 
is a more or less rigid, plastico-frangible, unshrinking crust upon a 
plastico-rigid, shrinking interior. Between the central sphere and 
its crust, adjustment is made possible by a zone of almost no 
strain, above which the earth’s crust must undergo strain increas- 
ing from near zero at the base to a maximum at the surface.* 
Within the zone of flow the strain is accommodated by flow, above 
that by a combination of flow and shearing.2 Any thrust that 
may be applied in a zone of perfect flow cannot be transmitted as 
such; it is transmitted hydrostatically. However, it is not prob- 
able that there is a zone of perfect flow; probably the rock yields 
under long-continued pressure, whereas, in the manner of tar, it 
might rupture under a sudden shock. Such shocks are incon- 
ceivable as affecting this zone of flow, and for purposes of this dis- 
cussion the zone of flow may be regarded as one in which there is 
a minimum of vector or directional forces. Movement of the 
crust over the shrinking interior would tend to produce displace- 
ment in the zone of flow at an angle approaching zero, no matter 
at what angle thrust forces cause rupture in the upper crust. 

A perfectly rigid body transmits thrust in such a way that the 
forces are not dissipated during transmission. - This type of body 
does not obtain in the earth’s crust, for rocks are not perfectly 
rigid materials. Material which is slightly plastic tends to fail 
near the points of the application of force instead of near the 


*T. C. Chamberlin and R. D. Salisbury, Geology, II (1907), 127-30. 
2C. K. Leith, Structural Geology (1913), p. 4. 
3T. C. Chamberlin, “‘The Problem of Faulting,’ Econ. Geol., II (1907), 597-909. 


CONCERNING THE PROCESS OF THRUST FAULTING 421 


_ center, the part most susceptible in nearly rigid members. Never- 
theless, the rocks within a mile of the earth’s surface are, in general, 
more nearly rigid in behavior than those near the zone of flow. 
Furthermore, there is more force to be transmitted presumably 
near the surface, because the length of the arc is greater at the 
surface than near the center, and the accumulative forces are pro- 
portional to the length of the arc to be accommodated to the 
shrinking. Consequently, there is a greater thrust transmitted 
in the rocks near the surface than through those near the zone of 
flow for two reasons, because the rocks are more nearly rigid, 
transmitting a greater proportion of the forces extant, and because 
near the surface there is more total horizontal force to be trans- 
mitted. ‘These conditions may be analyzed as an unequally dis- 
tributed force of the rotational type. Since the strain is greatest 
where relief of pressure is easiest, it follows that the strain is 
greater near the surface than at depth, which would result in a 
rotational strain even if the forces were translatory.’ Thus rota- 
tional strain results from a ready relief of pressure near the 
surface, and it appears reasonable that the original stresses applied 
also are rotational. 

The length of the crustal members.—The commonly deformable 
crust is considered to be a discontinuous structure in the form of 
a supported hollow sphere composed of irregularly shaped, curved 
strata plates which are geographically coincident with the con- 
tinental and oceanic segments. ‘These members of the structure 
exert thrust forces on one another which are localized in their 
maximum application at the planes of contact, ie., the border- 
land of continents and oceans. Roughly speaking, the members 
involved in the compression are as long as the continents and 
ocean basins are wide. The forces, however, are not of equal 
intensity everywhere along the length of each member; under 
normal conditions they are least in the center and greatest at the 
ends. If the earth’s crust were truly rigid the intensity of thrust 
would be equal throughout the length of each member, each seg- 
ment would serve as a footing for its neighboring segments, result- 
ing in failure of the segments near their centers. Apparently the 


1F, D. Adams and J. A. Bancroft, Jour. Geol., XXV (1917), 637; R. T. Cham- 
berlin and W. Z. Miller, ibid., XX VI (1918), 35-37. 


422 TERENCE T. QUIRKE 


members fail near their ends probably due to the fact that forces 
are not transmitted well through partly deformable members. 
The condition of a single member may be represented as in Figure 1, 
in which it is indicated that the thrust decreases from a maximum 
at the edges of the continental and oceanic segments to a minimum 
near their centers. Part of the force is absorbed in minor defor- 
mation of the member and only part is transmitted; therefore, 
the increase of force toward the end of the members is not one of 
arithmetical progression. ‘Thus the yielding of the earth’s crust 
permits the stresses relief, so that at one time the intensity of 






North America 





Fic. 1.—Diagram to illustrate the supposed distribution of transmitted crustal 
stresses. The top line is supposed to represent graphically the magnitude of the 
transmitted stresses. The transmitted stresses vary from a minimum near the 
centers of the oceanic and continental segments to zones of maximum intensity near 
the borders of the continents. 


thrust on one side of a yielding section is much greater than the 
intensity of thrust on the other side of the yielding section. This 
condition results in a movement of part of the member in the direc- 
tion of the lower intensity of thrust. ‘This direction of movement 
is commonly said to be the direction of the deforming force. How- 
ever, action and reaction being equal and opposite, the direction 
of any force must be two-faced. But whatever the direction of 
movement, either toward or from the continental masses, the 
continental masses exert just as great a thrust upon the oceanic 
masses as they bear themselves. Consequently there must be 
a tendency for the oceanic masses to suffer deformation, 
especially near the continents. ‘There is supposed to be a region 
or band of great stress at the borders both of oceanic and conti- 
nental masses, within which major deformation should be expected. 


CONCERNING THE PROCESS OF THRUST FAULTING 423 


Let it be noted, however, that this band of great stress is supposed 
to be but a part of the total member under compression. 

The depth of the crustal members.—According to Chamberlin 
and Salisbury" (writing in 1904) the average thickness of the 
folded shell is probably between three and five miles. From the 
context it appears that the estimate was based, in part at least, 
upon a reconnaissance report on the amount of uplift and shorten- 
ing involved in the Appalachian folding, and the resulting figure 
probably should be modified especially by the results of R. T. Cham- 
berlin before quoted, as well as by the many contributions based 
upon experiments made since 1904. Heim concludes from his 
studies in the Alps that there the great deformations were rela- 
tively shallow in extent. In 1912 F. D. Adams reported that 
open cavities might persist in rocks at depths of at least eleven 
miles,? from which it appears that the zone subject to fracture and 
flow, or plastico-frangible deformation, might be deeper than 
usually expected. But from his work in association with Ban- 
croft, Adams finds that the amount of thrust required to produce 
deformation increases rapidly with the increase in depth, and 
therefore concludes that the transference of material at the earth’s 
crust must take place comparatively near the surface. Bridg- 
man,’ who subjected metal pieces to pressures comparable to 
those that are supposed to obtain at depths of between twenty 
and seventy miles, agrees that substances tend to become more 
rigid under high pressures, but reports further that under great 
pressures there is no relation between the yield and rupture points, 
for there is no rupture point. Materials (metals at least) deform 
without rupture, although they remain highly rigid. This is the 
condition supposed to be characteristic of the great interior of the 
earth, which is therefore called plastico-rigid.® 

1Op. cit., p. 126; cf. Bailey Willis, U.S. Geol. Surv., 13th Ann. Rept., Part II 
(1891-92), p. 228. 

2¥F, D. Adams, Jour. Geol.,,XX (1912), 97-118. 

3 Frank D. Adams and Austin J. Bancroft, ibid., XXV (10917), 635. 

4P, W. Bridgman, Phil. Mag. (July 1912), p. 65; see also Phys. Review, XXXIV 

Tote) Ma cAc s 

s A later paper by Bridgman has further bearing on the probable plastico-rigid 

behavior of the interior, ‘‘On the Effect of General Mechanical Stress on the Tem- 


perature of Transition of Two Phases, with a Discussion of Plasticity,” Phys. Review, 
New Series, VII (1916), 215-23. See also Joseph Barrell, op. cit., pp. 431-32. 


424 TERENCE T. QUIRKE 


All these researches seem to indicate that the zone of fracture, 
folding, and of deformation in general which may be called plastico- 
frangible is probably confined to depths which properly may be 
called shallow. 

T. Mellard Reade™ used the terms sheet or strata-plate to 
describe the deformable parts of the earth’s crust, and Chamberlin 
and Miller? suggest that the deformation of some folded mountain 
chains is perhaps analogous to the deformation of a thin prism or 
wall. 

Probably few geologists would maintain that the frangible 
part of the earth’s crust is more than fifteen miles deep. 

The probability of crustal members as such.—Thus, the crustal 
members are conceived to be sheets conforming to the curvature 
of the earth, from 200 to 300 times as wide and long as they are 
thick. Their proportions may be compared to those of a pave- 
ment one foot thick covering a city block about three. hundred 
feet square. This conception of strata-plate members of great 
length and width might appear unreasonable were it not for the 
fact that each member is not an unsupported arch. Each member 
is very appreciably stiffened by the support of the plastico-rigid or 
elastico-rigid mass. beneath. 

A consideration of the probable effects of the yielding of such 
members is interesting. Supposing that there should be moun- 
tain folding near the border of a continent, the yielding decreases 
the stresses at the place of failure and throughout a certain dis- 
tance on either side. Were the crust rigid instead of plastico- 
frangible, the stresses would be relieved throughout the whole of 
the neighboring sections, and the stress relief would be distributed 
promptly throughout all the members of the earth’s crust. Thus, 
distribution of relief would tend to become world-wide, but the 
plastic-like behavior of the members retards such a distribution of 
stress and in some cases absorbs it within a relatively short dis- 
tance. In such cases conditions for the continental mass may 
include a relieved, small, residual stress on one side of the conti- 
nent and a large, almost unrelieved stress on the other side of the 
continent. This may result in a later break on the unrelieved 

1T. Mellard Reade, The Evolution of Earth Structure (1903), p. 134. 

2 OD. cit., p. 21. 


CONCERNING THE PROCESS OF THRUST FAULTING 425 


side of the continent or may give rise to further slow adjust- 
ments affecting the major part of the continental member. 
In short, the mutual bearing of the crustal members upon one 
another may be partly responsible for the usual, very wide- 
spread epirogenic movements which follow mountain folding. 
These conceptions may appear at first glance to be clearly reac- 
tionary and out of accordance with modern views based on the 
research and studies of the last twenty years, especially with the 
conceptions of T. C. Chamberlin,’ who discusses deep, rigid earth 
cones separated from one another by shear zones, but so far as is 
_ known to the writer these ideas are not necessarily in conflict with 
such conceptions of the earth’s interior. It should be emphasized 
that the writer’s suggestions are based on the assumption, which 
seems to be widely accepted, that there is a crustal member, sub- 
ject to fracture and flow, separated from the underlying plastico- 
rigid interior by a zone of shearing or flow. The recognition of 
this zone of separation causing the crust and the inner mass at 
certain times to be a discontinuous member, the parts of which 
are subject to separate analysis, is absolutely fundamental to this 
discussion. It may be that this zone of shearing is merely an 
occasional phenomenon coming into being only as the result of 
more fundamental processes,*and that its depth (and in conse- 
quence its competence) may vary from time to time with differ- 
ent periods of stress, and it is likely that the development of such 
a zone to an extent comparable with the width of a continent is 
an extreme and unusual condition. And it must be recognized 
that the writer advances this study as a contribution to the analysis 
of low-angle faulting, in its proper relation to the other factors 
listed by Chamberlin and Miller? in the résumé of their paper 
previously quoted, with this difference, arising largely from the 
different manner of approach, that the writer would not list 
“length of deformed area with respect to its other dimensions 
(after analogy of long column)” among the minor factors, but 
rather among the major factors in low-angle faulting. Neverthe- 
less, it is held to be but one of several major factors. The revision 
1 The Origin of the Earth (1916), chap. viii, and Jour. Geol., XXVI (1918), 197. 
2 Jour. Geol., XXVI (1918), 44. 


426 TERENCE T. QUIRKE 


of the proportions of the crustal units, the abandonment of any 
idea of those members being unsupported arches, the recognition 
that they are probably relatively temporary phenomena coming 
into being*only upon occasion, and the limitation of this discussion 
to those members subject to fracture put this conception of strata- 
plate members in an entirely different class from the old theory of 
crustal members which Chamberlin and Salisbury’ emphatically 
discarded long ago. 

A comparison of the crustal members with sheets and long columns. 
—Euler’s formula? has been used in comparing the deformation of 
sheetlike members of the earth’s crust to the yielding and failure | 
of long columns because the failure of sheets is similar to that of 
long columns and because analyses of the deformation of sheets 
under lateral thrust are rare or wanting. Euler’s formula applies 
strictly only to columns having lengths many times greater than 
their least diameter. Of course this formula is used merely as an 
illustration of the order of magnitude of the strength of a sheet. 
It is not accurate to apply it even to every long column; yet it 
applies with appropriate empirical modifications to all long columns. 

W.H. Burr’ says: ‘‘ Pieces of material subjected to compression 
are divided into two general classes—‘short blocks’ and ‘long 
columns’; the first of these only, afford phenomena of pure com- 
pression. A ‘short column’ is such a piece of material, that if it 
be subjected to compressive load it will fail by pure compression. 
On the other hand, a long column (as has been indicated in Art. 25) 
fails by combined compression and bending... . . The length of a 
short block is usually about three times its least lateral dimension.”’ 

Therefore it is concluded that the earth’s crust in major defor- 
mation follows closely the behavior of long columns because it 

*T. C. Chamberlin and R. D. Salisbury, Geology, I (1904), 554-62. 


2T. T. Quirke, Geol. Survey, Canada, Mem. No. 102, “ Espanola District, Ontario” 
(t917),p. 71, and Chamberlin and Miller, op. cit.,p.19. According to Euler’s formula 
the strength of a column equals 

1 
EI Ta? 

in which E equals the coefficient of elasticity of the material involved, J equals the 
moment of inertia, and Z equals the length of the column. 

3.W.H. Burr, The Elasticity and Resistance of the Materials of Engineering (18090), 
Dials 


f 


CONCERNING THE PROCESS OF THRUST FAULTING 427 


appears to yield first by flexure and then by rupture, and that 
many experiments performed by Willis, Cadell, Chamberlin, 
Miller, and others, technically speaking, are experiments with 
long columns rather than with short blocks, because the members 
flexed before rupturing. More strictly speaking, most of these 
experiments on deformable materials fall under the mechanical 
analyses of neither short blocks nor of long columns because of 
the nature of the material, but they seem to accord the more 
closely to long-column analysis. If an adequate amount of experi- 
mental and analytical work had been done upon the deformation of 
sheets,’ the writer would have used only the sheet as an illustra- 
tion of earth deformation. 


THE RUPTURE OF SHEETS AND LONG COLUMNS 


Experiments with sheets under rotational stress.—In hope of 
learning more about the deformation and rupture of sheets the 
writer performed a few simple experiments upon easily controlled 
members. ‘T. Mellard Reade has done sufficient work with straight 
and circumferential compression upon sheets, but the effects of a 
vertically unequally distributed stress heretofore have not been 
tried. Reade? draws conclusions from the deformation of the lead 
lining of a scullery sink. The writer used a common bench vise 
to deform and rupture plates of soap and paraffin. Of the two, 
soap was the more satisfactory. In order to secure an unequally 
distributed stress a wedge was inserted, large end upward, between 
the end of the member and the face of the vise. This resulted in 
bringing greater pressure to bear near the top than near the bottom 
of the plate. If the plate had been quite free to bend it would 
have bent downward; however, that would not have illustrated 
the deformation of rock strata, and the member was therefore 
stiffened enough by slight pressure from below to make it bend 
upward. After the bending of the soap, rupture started from the 
bottom at a low angle from a point nearly equidistant from each 


«The only work known to the writer which appears to have a bearing on the 


subject is “Tests of Reinforced Concrete Flat Slab Structures,” by Arthur N. Talbot 


and Willis A. Slater, University of Illinois Bull., Vol. XIII, No. 22, 1916. 
2T. Mellard Reade, The Origin of Mountain Ranges (1886), pp. 15-16, and 
Plate VL p.: 28. ‘ 


428 TERENCE T. QUIRKE 


side, became nearly horizontal near the center, and increased to 
nearly 60° as it approached the upper surface (Fig. 2). ‘To prove 
that this is the usual type of break and not fortuitous, two more 
pieces of soap were flexed and broken with similar results. Two 
narrow pieces of soap broke with nearly vertical shear planes near 





Fic. 2.—(a) A sheet of soap ruptured by combined compression and bending 
under rotational stress. The fault plane is high-angled near the surface and low- 
angled below the center of the member. (These pieces are outlined in Figure 3. (b) A 
sheet of paraffin ruptured by combined compression and bending under rotational 
stress. The fault plane is almost horizontal for most of the length, changing sharply 
at a high angle to the surface. At one end the member is split down the center along 
the plane of maximum shear without actual breaking out of the piece; see also Figure 5, 


(a) and (0). 


the edges (Figs. 2 and 3), but a plate wider than it is long ruptured 
without vertical shear planes at a low angle (Fig. 4). It seems 
that nearly vertical fault planes may be disregarded, occurring 
merely because the sheets are narrow and have lateral relief. In 
the case of earth deformations in general, the width of the sheet 
or strata-plate is probably comparable to the length of the defor- 


CONCERNING THE PROCESS OF THRUST FAULTING dee 


imation member, and vertical fault Pane of a comparable origin 
are not commonly recognized. 

Experiments with short blocks under rotational stress.—Experi- 
ments with paraffin led to somewhat different results. The 





Fic. 3.—(a) and (5) are two views of a sheet of soap which failed by combined 
compression and bending under rotational stress. The em e of the piece of 
soap are fy X43 X24 inches. The contour intervals are ; inch, indicating the plane 
of rupture. A photograph of the piece is en ee ESO in Figure 2. (c¢) is a cross- 
section of another piece of soap showing a similarrupture. The dimensions are 75 X 4° 


x 275 inches. 


paraffin members did not flex so readily as soap, and therefore, in 
spite of their dimensions, they approach the behavior of short 
blocks under the conditions of these experiments. The members 
did not break from the bottom to top but after a few preliminary 
high-angle slice faults part of the members seemed to chip out 
(Fig. 5, c and d), illustrating the manner in which weak unbend- 
ing blocks yield under a rotational compression.’ However, having 


t In experimental engineering any cement block which is loaded with an unequally 
distributed load fails by breaks, making low angles with the direction of applied force. 
Such breaks are considered faulty, because the object of that work is to determine the 
strength of the blocks under equally distributed stress. 


430 TERENCE T. QUIRKE 
@ 

flexed slightly, one paraffin member started to split down the 
center along a plane parallel to the surface in the manner of a 
bending column (Figs. 5 and 2). 

Chamberlin and Miller had obtained similar low-angle breaks 
when they caused rotational strain in a paraffin short block, 
thereby proving their contention in favor of the importance of 
rotational strain as a cause of low-angle faulting. The writer 


~~ er —- 
Sat 


~~ 


¢ 
’ 
' 


SS et aces 
= ae oe 
™~= 


PA en ne 





Fic. 4.—A wide sheet of soap which failed under rotational stress by combined 


compression and bending. ‘The dimensions of this piece are 2;45%4X 49 inches and 


the contour lines are equidistant. ‘They indicate the place of rupture. 


has used a rotational stress and bending sheets rather than short 
blocks in order to be consistent in the general treatment and 
object of the paper and for the sake of the mechanical considera- 
tions which are treated later. , 

Analysis of the rupture of sheets and columns under translatory 
forces.—Long columns and sheets fail by bending and by rupture 


t Jour. Geol., XXVI (1918), 35, and Fig. 16. 


CONCERNING THE PROCESS OF THRUST FAULTING 431 


under continued compression. A column may crumple into many 
folds or it may spring out into a single arch. The second case is 
stable for unsupported columns, but in the case of the earth’s 
crust the formation of many folds is common. Mechanically the 
analysis of the stresses in one fold of a series is the same as that in 
a single arch. The maximum tensional stress is at the apex of the 





Fic. 5.—Paraffin members which failed under rotational stress. (a) and (0) 
are two views of a piece 485 X 3455 X 2145 inches in size, which yielded by combined com- 
pression and bending. Compare Figure 2 and note the place of rupture along the 
plane of maximum shear parallel to the surface. (c) is a side view of a piece 4°9 X 4;°y 
X 2 7% inches which seemed to fail by mere compression; the break indicated by dotted 
lines followed several high-angle breaks. (d) is a side view of a piece 4% X 24°55 X 21% 
inches in size which ruptured without flexing. Note the tendency toward high- 
angle breaks. 


arch at the surface, the maximum compression beneath the apex 
of the arch at the bottom of the deformed member, the focus of 
maximum shear a plane containing the axis of the member and 
parallel to the plane of greatest length and width of the member 
(Fig. 6B, S—S). A bending member which yields to shear alone 
splits from end to end along a plane of maximum shear, a similar 


432 TERENCE T. QUIRKE 


member yielding to tension parts in a plane at right angles to its 
axis. Figure 7 illustrates the rupture of flexed wooden columns 
by tension and shear. Examples A and B have ruptured by ten- 
sion and by shear, whereas example C has ruptured by a com- 
bination of tension and shear. Applying these illustrations to 
conditions in the earth’s crust, it is probable that rock is so weak 
to resist tension that under continued straight compression its 
folds are likely to rupture at the arches by tension. In the case 





Fic. 6.—A illustrates the character of rupture of a short block under highly 
rotational compression. The surface abcd represents the break. The planes marked 
x represent the distributed shear due to the unequally distributed forces F. B illus- 
trates the character of rupture of a long column or of a flexible sheet by rotational 
compression. The plane marked S is the plane of maximum shear due to flexure; 
the planes marked « indicate the planes of distributed shear and the action of the 
unequally distributed forces F. The place of maximum tension is marked ¢ and 
the place of maximum compression is marked k. The rupture abcd ideally follows 
the plane S—S partly and emerges near t. 


of major terrestrial deformations, however, straight compression 
is thought to give place to rotational forces, and the situation 
is changed. 

Analysis of the rupture of sheets and columns under rotational 
forces.—Any compressive force unequally distributed in its appli- 
cation gives rise to shearing stresses within the member affected. 
The case of members folded by rotational forces includes tension 
due to bending, shear due to bending, and shear due to rotational 
stress. The plane of maximum shear is somewhere near the middle 


CONCERNING THE PROCESS OF THRUST FAULTING 433 


of the member (Fig. 6), and the tendency to shear due to rotational 
stress is distributed in parallel planes, one of which must coincide 
with the plane of maximum shear due to folding. Thus rotational 
stress adds a tendency to shear along the plane of maximum shear 
already developed by folding. This explains the low-angle breaks 





ad 


Fic. 7.—The rupture of flexed wooden columns by tension and shear. Under 
flexure, columns tend to split from end to end due to shearing, and to part in a plane 
at right angles to their long axes above the plane of shear by tension. Tension is 
greatest at the top of the arch, and shear is greatest along the center of the member. 
A and B show separate breaks due to shear and tension and C shows rupture induced 
by a combination of shear and tension. 


near the center of the slightly flexed paraffin sheet (Figs. 2 and 5), 
and the suggestion of a very low-angle break near the center of 
the ruptured soap (Figs. 2 and 4). 

Contemporaneous with this tendency to shear along a plane 
parallel to the axis of the deformed member, there is a lesser 
tendency to rupture by tension. The tensional break approaches 
a plane normal to the top of the arch, at right angles to the plane 
of maximum shear (Figs. 6.and 74 and B). A combination of 
these two is a plane which sweeps through a considerable change of 


434 TERENCE T. QUIRKE 


position amounting to go° in extreme cases. Such a combination 
is illustrated in the breaking of one wooden piece (Fig, 7C) and 
in the rupture of the soap and paraffin (Figs. 2, 3, 4, and 5). 

Comparisons between geological thrust deformations and members 
ruptured by rotational stress——In cases where rock members are 
subjected to both tension and shear we expect failure to be due to 
that which the rock is least able to withstand, that is, a combina- 
tion of both shear and tension. Rocks are strong to resist com- 
pression, and failure of rock members by straight compression 
needs little consideration when either great shear or great tension 
is involved. 

Comparisons between the rupture of these members which 
fail by combined compression and bending, the rupture of short 
blocks which fail by pure compression, and the geological relations 
of overthrust and reverse faults seem to suggest that many thrust 
faults may have resulted from the yielding of flexed members 
which have failed along planes of shear and tension, members of 
the class of long columns. : 

Thus it appears that some members under terrestrial compres- 
sion are curved sheets or strata-plates, which are thin in compari- 
son with their width and length; being subjected to an unequally 
distributed rotational stress they break normally along shear 
planes of low angles at depths which steepen to high angles due to 
tension near the surface. 


KINETICS OF THRUST FAULTING 


Analysis of the conditions following’ rupture and preceding dts- 
placemeni.—Some rotational force deforms the terrain by flexure. 
If the folding is sharp no fold can transmit thrust because the fold 
must fail at the crown of the arch due to localized tension. Rock 
is incompetent to carry tensional stresses, and therefore a high 
arch fails under lateral compression. If the arch fails, no appreci- 
able thrust can be transmitted until folding has reached an isoclinal 
condition, involving great shortening, great thickening, and thereby 
great strengthening of the member.t This case is extreme and 
must be rare. More commonly the folds are so low that thrust 


tC Quirke yop, vite piv7 2° 


CONCERNING THE PROCESS OF THRUST FAULTING 435 


can be transmitted without rupture of the arches, and rupture 
follows the forms outlined above (Fig. 6). In an analysis of the 
conditions at the instant after rupture, let P be the total compres- 
sive force, let G be the weight of the moving mass, let © be the 
angle of shearing at any one place, and let a represent the cross- 
sectional area of the member. Then, as Chamberlin and Miller 
show,’ the intensity of thrust (p,) tangential to the shear plane is 


Psin9cos® 
pia F 





and the intensity of the normal stress (p,) is 
Wisin? O 
cea 
a 
Likewise, the force of gravity is resolved into tangential and nor- 
mal components, the tangential opposing the tangential compo- 
nent of the thrust, and the normal being added to the normal 
component of the thrust. The tangential component of gravity is 
G,;=G x sin 0, 
and the normal component is 
G,=G ¥ cos. 0: 
The intensity of the tangential component of gravity is 
GsinO G 


=—sinOtan®@. 
acotO® a 





Li 


The intensity of the normal component of gravity is 


GcosO'lG = 
= — =—sin®Q. 
acotO a 





1 


Thus, after rupture the intensity of thrust becomes 
PsinOcosO GsinOtanO_sin® 


(P cos 8—G tan 8), 
a a a 


and the intensity of friction becomes 
‘Asin OA kG 
Nee 


+2 sin 0) =p SEE (P sin0-+G), 


in which. represents the coefficient of kinetic friction. 
t Jour. Geol., XXVI (1918), 15 ff. 


436 TERENCE T. QUIRKE 


In order to achieve displacement, 


P sin 9 cos 0 
a 





must be sufficiently greater than 


Gsin 9 tan 0 
a 





to overcome the friction due to both the normal component of 
thrust and the normal component of gravity. The friction will 
become less per square unit of fault plane as slickensides and 
other smooth surfaces are developed by movement. But the total 
area of friction increases with displacement, and it follows from 
the preceding formulas that friction is greatest in intensity where 
0, the angle of displacement, is greatest. 

The fault plane decreases in steepness as displacement increases.— 
Rupture being accomplished, as indicated in Figure 6B, the fault 
plane varies from places of low dip far beneath the surface to 
places of high dip nearer the surface. Where the angle is low the 
tangential thrust is greatest, the normal component of thrust is 
least, but the normal component of gravity is a maximum, and 
the resistant, tangential component of gravity is a minimum. 
Near the surface where the angles are high and the normal compo- 
nent of gravity is low, the resistant tangential thrust due to gravity 
is a maximum and the tangential component of the compres- 
sive force is a minimum, but its frictional component is a maxi- 
mum. In all these movements the compressive thrusts must be 
dominant, otherwise the force of gravity and friction would pre- 
vent displacement. ‘Therefore, displacement being granted, the 
effect of gravity is not vital in the discussion. Obviously, then, 
the effects of thrust result in a maximum shear along low-angled 
planes and a maximum friction at high-angled planes. 

In the general case of rupture represented in Figure 6B maxi- 
mum friction is near the surface. The hanging wall of millions of 
tons of rock moving several miles along this fault plane will result 
in enormous abrasion, much as a glacier abrddes greatly the stoss 
sides of steep opposing hillsides, and this abrasion will be greatest 


CONCERNING THE PROCESS OF THRUST FAULTING 437 


where friction is greatest, at the steepest part of the plane, affect- 
ing both the footwall and ‘the hanging wall. During early dis- 
placement the fault will appear at the surface as a steeply dipping 
plane; by the time displacement has continued for a mile, the 
angle of the fault plane must have been worn flatter by the friction 
of the moving load; finally, by the time displacement has attained 
a few miles, the low-angled sole will have reached the surface, and 
the fault plane must have been reduced to a low angle by abrasion, 
leaving no trace of the steep parts of the original break. 

In this manner it is suggested that all great thrust faults which 
are steep-angled near the surface, if persistent in depth, follow 
the low-angle form at the depth of a few miles, and that in a general 
case the angle of faulting at the surface may depend as much 
upon the amount of displacement subsequent to rupture as upon 
fundamentally different conditions in the application of earth 
forces or in the character of the members affected. In support of 
this it may be recalled that, so far as is known regarding thrust 
faults, all faults of great displacement have low-angle fault planes, 
and no faults of high angles exceed a few miles in displacement. 

Willis' has described rotated, high-angle thrust faults of rela- 
tively small throw in the coast ranges and the Sierra Nevada, 
which he considers to have some such shape as is here suggested 
for thrust faults of small displacement; however, his explanation 
of their character differs considerably from the general argument 
of this paper. « 

CONCLUSION 

In conclusion some repetitions seem pertinent. Certain parts 
of the earth’s crust which are deformed by regional compression 
are held to be analogous to sheets and comparable in mechanical 
analysis to long columns. The normal terrestrial stress is said to 
be an unequally distributed thrust of rotational type. The trans- 
mission of stress as a vector quantity supposedly extends from the 
surface to a depth scarcely exceeding fifteen miles. There is a 
zone of potential separation between the frangible crust and the 
rigid interior which is nearly parallel to the surface. In some 
cases thrust faults of very great displacement may be extensions 


1 Bailey Willis, Geol. Soc. Amer. Bull., XXX (1919), 84-86. 


438 TERENCE T. QUIRKE 


of this low-angle zone of parting to the surface at an increasing 
degree of steepness;' in other cases rupture occurs within the 
bending part of the crust near the plane of maximum shear with a 
break low-angled at depth and increasing in steepness near the 
surface. In either case displacement of less than one mile results 
in a steep-angle fault, an ordinary reverse fault, but displacement 
of several miles results in reduction of steepness of the fault plane 
' by the abrasion of the footwall and by advancement of the low- 
angle part of the hanging wall to the surface. Thus some 
low-angle overthrust faults and high-angle reverse faults may 
represent different stages of a single process. 


*T. C. Chamberlin, Econ. Geol., II (1907), 597-99. 











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